### Abstract

In the study of open quantum systems, one typically obtains the decoherence dynamics by solving a master equation. The master equation is derived using knowledge of some basic properties of the system, the environment, and their interaction: One basically needs to know the operators through which the system couples to the environment and the spectral density of the environment. For a large system, it could become prohibitively difficult to even write down the appropriate master equation, let alone solve it on a classical computer. In this paper, we present a quantum algorithm for simulating the dynamics of an open quantum system. On a quantum computer, the environment can be simulated using ancilla qubits with properly chosen single-qubit frequencies and with properly designed coupling to the system qubits. The parameters used in the simulation are easily derived from the parameters of the system + environment Hamiltonian. The algorithm is designed to simulate Markovian dynamics, but it can also be used to simulate non-Markovian dynamics provided that this dynamics can be obtained by embedding the system of interest into a larger system that obeys Markovian dynamics. We estimate the resource requirements for the algorithm. In particular, we show that for sufficiently slow decoherence a single ancilla qubit could be sufficient to represent the entire environment, in principle.

Original language | English |
---|---|

Article number | 062317 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 83 |

Issue number | 6 |

DOIs | |

Publication status | Published - 14 Jun 2011 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*83*(6), [062317]. https://doi.org/10.1103/PhysRevA.83.062317

**Quantum algorithm for simulating the dynamics of an open quantum system.** / Wang, Hefeng; Ashhab, Sahel; Nori, Franco.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 83, no. 6, 062317. https://doi.org/10.1103/PhysRevA.83.062317

}

TY - JOUR

T1 - Quantum algorithm for simulating the dynamics of an open quantum system

AU - Wang, Hefeng

AU - Ashhab, Sahel

AU - Nori, Franco

PY - 2011/6/14

Y1 - 2011/6/14

N2 - In the study of open quantum systems, one typically obtains the decoherence dynamics by solving a master equation. The master equation is derived using knowledge of some basic properties of the system, the environment, and their interaction: One basically needs to know the operators through which the system couples to the environment and the spectral density of the environment. For a large system, it could become prohibitively difficult to even write down the appropriate master equation, let alone solve it on a classical computer. In this paper, we present a quantum algorithm for simulating the dynamics of an open quantum system. On a quantum computer, the environment can be simulated using ancilla qubits with properly chosen single-qubit frequencies and with properly designed coupling to the system qubits. The parameters used in the simulation are easily derived from the parameters of the system + environment Hamiltonian. The algorithm is designed to simulate Markovian dynamics, but it can also be used to simulate non-Markovian dynamics provided that this dynamics can be obtained by embedding the system of interest into a larger system that obeys Markovian dynamics. We estimate the resource requirements for the algorithm. In particular, we show that for sufficiently slow decoherence a single ancilla qubit could be sufficient to represent the entire environment, in principle.

AB - In the study of open quantum systems, one typically obtains the decoherence dynamics by solving a master equation. The master equation is derived using knowledge of some basic properties of the system, the environment, and their interaction: One basically needs to know the operators through which the system couples to the environment and the spectral density of the environment. For a large system, it could become prohibitively difficult to even write down the appropriate master equation, let alone solve it on a classical computer. In this paper, we present a quantum algorithm for simulating the dynamics of an open quantum system. On a quantum computer, the environment can be simulated using ancilla qubits with properly chosen single-qubit frequencies and with properly designed coupling to the system qubits. The parameters used in the simulation are easily derived from the parameters of the system + environment Hamiltonian. The algorithm is designed to simulate Markovian dynamics, but it can also be used to simulate non-Markovian dynamics provided that this dynamics can be obtained by embedding the system of interest into a larger system that obeys Markovian dynamics. We estimate the resource requirements for the algorithm. In particular, we show that for sufficiently slow decoherence a single ancilla qubit could be sufficient to represent the entire environment, in principle.

UR - http://www.scopus.com/inward/record.url?scp=79961057098&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79961057098&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.83.062317

DO - 10.1103/PhysRevA.83.062317

M3 - Article

VL - 83

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 6

M1 - 062317

ER -